Drilling down: the origins of strength and ductility 121

6.4 Drilling down: the origins of strength and ductility 121

defects. All crystals contain vacancies, shown in (a): sites at which an atom is missing. They play a key role in diffusion, creep and sintering (Chapter 13), but we don’t need them for the rest of this chapter because they do not influence strength. The others do.

No crystal is totally, 100%, pure and perfect. Some impurities are inherited from the process by which the material was made; more usually they are delib- erately added, creating alloys: a material in which a second (or third or fourth) element is dissolved. ‘Dissolved’ sounds like salt in water, but these are solid solutions. Figure 6.10(b) shows both a substitutional solid solution (the dissolved atoms replace those of the host) and an interstitial solid solution (the dissolved atoms squeeze into the spaces or ‘interstices’ between the host atoms). The dis- solved atoms or solute rarely have the same size as those of the host material, so they distort the surrounding lattice. The red atoms here are substitutional solute, some bigger and some smaller than those of the host; the cages of host atoms immediately surrounding them, shown green, are distorted. If the solute atoms are particularly small, they don’t need to replace a host atom; instead, they dissolve interstitially like the black atoms in the figure, again distorting the surrounding lattice. So solute causes local distortion; this distortion is one of the reasons that alloys are stronger than pure materials, as we shall see in a moment.

Now to the key player, portrayed in Figure 6.10(c): the dislocation. ‘Dislocated’ means ‘out of joint’ and this is not a bad description of what is happening here. The upper part of the crystal has one more double-layer of atoms than the lower part (the double-layer is needed to get the top-to-bottom registry right). It is dislocations that make metals soft and ductile. Dislocations distort the lattice—here the green atoms are the most distorted—and because of this they have elastic energy associated with them. If they cost energy, why are they there? To grow a perfect crystal just one cubic centimeter in volume from a liq-

uid or vapor, about 10 23 atoms have to find their proper sites on the perfect lattice, and the chance of this happening is just too small. Even with the great- est care in assembling them, all crystals contain point defects, solute atoms and dislocations.

Most contain yet more drastic defects, among them grain boundaries. Figure 6.10(d) shows such boundaries. Here three perfect, but differently oriented, crystals meet; the individual crystals are called grains, the meeting surfaces are grain boundaries. In this sketch the atoms of the three crystals have been given different colors to distinguish them, but here they are the same atoms. In reality grain boundaries form in pure materials (when all the atoms are the same) and in alloys (when the mixture of atoms in one grain may differ in chemical com- position from those of the next).

Now put all this together. The seeming perfection of the steel of a precision machine tool or of the polished case of a gold watch is an illusion: they are rid- dled with defects. Imagine all of the frames of Figure 6.10 superimposed and you begin to get the picture. Between them they explain diffusion, strength, ductility, electrical resistance, thermal conductivity and much more.

So defects in crystals are influential. For the rest of this section we focus on

122 Chapter 6 Beyond elasticity: plasticity, yielding and ductility

Slip vector

b Extra half-plane

Slip vector

Extra half-plane

Slip plane

Slip plane

Slipped area

Edge dislocation line

(a)

(b)

Figure 6.11 (a) Making a dislocation by cutting, slipping and rejoining bonds across a slip

plane. (b) The atom configuration at an edge dislocation in a simple cubic crystal. The configurations in other crystal structures are more complex but the principle remains the same.